Numerical Variables

Using the information_gain() function, we can evaluate how much each variable reduces uncertainty in predicting the target variable PRICE. The analysis indicates that REQUESTED_SIZES, BID_WON, and AUCTION_ID contribute the most information gain, while nearly all other variables exhibit relatively low, and roughly similar, values. Notably, the Region variable provides minimal information gain, which is expected given that the dataset is entirely restricted to Oregon.

Price

The histogram of bid prices is peaks greatly to the left of the plot, indicating that most bids are low in value. The summary statistics reveal several extreme outliers that create a right-skewed distribution, with prices reaching up to $141.25. The boxplot highlights a median bid price of approximately $0.20, with an interquartile range from $0.07 to $0.57, showing that the vast majority of bids are below $1.

Summary Statistics for PRICE

Min	1st Q	Median	Mean	3rd Q	Max
7.1e-05	0.07	0.196	0.474	0.57	141.25

Response Time

The histogram of the Response Time variable exhibits a right-skewed distribution, with the mean response time of 201 milliseconds and a majority of observations falling between 50 and 400 milliseconds. The boxplot shows a median of 164 milliseconds and an interquartile range of 110 to 257 milliseconds. While the boxplot truncates numerous outliers, these higher values are evident in the histogram. Overall, the system typically responds quickly, with a smaller subset of observations exhibiting longer response times.

Summary Statistics for Response Time

Min	1st Q	Median	Mean	3rd Q	Max
10	110	164	201.536	257	1893

Device Geo Latitude

The majority of latitude values fall between 45 and 46 degrees, with the minimum observed value being 42 degrees. The distribution is slightly left-skewed, peaking around 45.5 degrees. The boxplot shows a median latitude of 45.514, with a narrow interquartile range from 45.3 to 45.525. These findings are consistent with the fact that the bid data were collected exclusively within Oregon.

Summary Statistics for Latitude

Min	1st Q	Median	Mean	3rd Q	Max
42.055	45.357	45.514	45.143	45.525	46.1879

Device Geo Longitude

The histogram of the longitude variable suggests an approximately normal distribution. A few outliers extend toward -118 degrees, but the majority of observations are concentrated around -122.5 degrees. The boxplot indicates a median longitude of -122.83, with an interquartile range from -122.83 to -122.59. This narrow span of 0.24 degrees captures the central 50% of the longitude values.

Summary Statistics for Longitude

Min	1st Q	Median	Mean	3rd Q	Max
-124.5055	-122.829	-122.64	-122.65	-122.589	-116.8578

Categorical Variables

Numerical vs Numerical

Numerical vs Categorical

Categorical vs Categorical

Conclusion

The analysis indicates that most bids are low in price, with a few extreme outliers producing a right-skewed distribution. Winning bids are consistently higher than losing bids, confirming that win rate is strongly associated with price. Device type and geographic location both influence bid price and response time, with Personal Computers and Tablets dominating the dataset. Although response time shows only minor variation across devices and regions, some outliers could affect bidding outcomes. High population areas, such as Portland, account for the majority of bids, yet median prices in these regions remain moderate.

Limitations

The analysis is limited by the dataset being restricted to Oregon, which may reduce the generalizability of findings to other regions. The high concentration of observations from Portland could skew overall results. Outliers in both price and response time introduce bias to mean-based measures, necessitating the use of medians for more robust insights. Additionally, two device type categories have some overlap, which may prevent a full understanding of the nuances in hardware or network performance.

Future Analysis

Future analyses could explore the causal factors influencing bid success, including device performance and response times. Expanding the dataset to cover a longer time period would allow for the investigation of temporal patterns in bidding behavior. Additionally, examining interaction effects between variables such as device type, geographic location, time of day, and bid price could provide deeper insights into the dynamics driving successful bids.